# Questions tagged [profile-likelihood]

The profile likelihood function is an inference function constructed from the likelihood function. If the likelihood function depends on many parameters and only some are of interest, then the other parameters are removed "by concentration", which means that they are "maxed out".

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### Profile Likelihood confidence interval

I am interested in obtaining profile likelihood confidence intervals for parameter identifiability. My cost function is the least square error between the data and some fitted approximation depending ...
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### Compare which of two groups is MORE similar to a third group?

I know I can use an ANOVA (+ post-hoc tests) to determine the equality (or inequality) of three groups: (i.e., H0: each of 3 means are equal; H A: at least 1 of 3 means is not equal). However, how ...
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### error code in finding confidence interval

I optimized parameters from a function using mle2 from bbmle package. After I got the values, I tried to find profile likelihood confidence interval of parameters using confint() but there is one ...
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### Confidence intervals for GLMM: bootstrap vs likelihood profile

I've built a relatively large negative binomial GLMM (~50000 observations, 10 covariates in conditional model, 1 covariate as zero-inflation model, 3 random intercepts (650, 26, 26 levels in each ...
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### Is the profile likelihood (dependent on one parameter) always a concave function?

Let $\theta = (\theta_1, \theta_2, \dots)$ be a vector of parameters, and let $L(\theta) = L(\theta|y)$ denote the likelihood function with respect to observed data $y$. Following the notation from ...
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### Confidence interval on the percentage difference of two binomial distributions

I have survey data for women and men following a binomial distribution. Their means are $p_1$ and $p_2$ respectively. I have calculated $(p_1-p_2)/p_2$ and would like to attach a confidence interval ...
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### Is my explanation of profile likelihood plots correct?

Using the metafor package in R to conduct a mixed-effects meta-analysis and meta-regression, I checked the profile likelihood ...
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### Confidence intervals with penalized likelihood

I am trying to perform parameter estimation using something like a maximum likelihood ratio method, however I need to add a penalty term to constrain nuisance parameters which describe certain ...
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### Existence and uniqueness of MLE

I am aiming to show that the MLE of $(\alpha, \lambda)$ for $X_1, \dots, X_n \sim \Gamma(\alpha,\lambda)$ exists and is unique, under the assumption that the $X_i$ are all positive and unequal. I am ...
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### Hessian of profile likelihood used for standard error estimation

This question is motivated by this one. I looked up two sources and this is what I found. A. van der Vaart, Assymptotic Statistics: It is rarely possible to compute a profile likelihood ...
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### What are the disadvantages of the profile likelihood?

Consider a vector of parameters $(\theta_1, \theta_2)$, with $\theta_1$ the parameter of interest, and $\theta_2$ a nuisance parameter. If $L(\theta_1, \theta_2 ; x)$ is the likelihood constructed ...
In my elementary statistics course, I learnt how to construct 95% confidence interval such as population mean, $\mu$, based on asymptotic normality for "large" sample sizes. Apart from resampling ...